0110274v2 16 Nov 2001

Associated tt¯H production at a VLHC: measuring the top-quark Yukawa coupling A. Belyaev∗ and L. Reina† Physics Department, Florida State University, Tallahassee, FL 32306-4350

F. Maltoni‡ Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (Dated: February 1, 2008)

arXiv:hep-ph/0110274v2 16 Nov 2001

Future hadron colliders will have the potential to measure some of the most relevant Higgs boson couplings with high precision. In this paper we investigate the potential of a Very Large Hadron Collider (VLHC) to measure the top-quark Yukawa coupling.

I.

INTRODUCTION

As part of the Snowmass effort to investigate the physics potential of future hadron colliders, we have addressed the problem of how some of the most relevant precision measurements of Higgs boson physics could benefit from the very high energy and statistics of these future facilities. We imagine a scenario in which one or more Higgs bosons have been discovered at either the Fermilab Tevatron or the CERN Large Hadron Collider (LHC), and a rich program of Higgs boson physics has already been developed. We then work under the assumption that precise determinations of the Higgs boson mass(es) and width(s), as well as determinations of various Higgs boson production cross sections, branching ratios, and ratios of Higgs boson couplings within a 10-20% uncertainty are available. The next generation of colliders will then play a crucial role in getting to a more precise determination of the Higgs boson couplings, therefore constraining its nature. It has been shown that an e+ e− Linear Collider, operating with high luminosity, can reach precisions of a few percents on all Higgs boson couplings except the Higgs boson self-couplings [1, 2]. The question is therefore what is the corresponding potential of a next generation hadron collider like a Very Large Hadron Collider (VLHC). Among the most important Higgs boson couplings, the Higgs-boson coupling to the top quark plays a special role. Because of the intriguingly large size of the top-quark mass, this coupling is largely enhanced with respect to all other Yukawa couplings and could shed some light on the obscure pattern of fermion mass generation and electroweak symmetry breaking. In this context, it is interesting to assess the precision with which the top-quark Yukawa coupling could be √ measured at a pp VLHC, running at center of mass energies of s = 40, 100, 200 TeV respectively. The golden mode for this measurement is the associated production of a Higgs boson with a pair of top-antitop quarks, pp → tt¯H, [3]. The Higgs boson is radiated either from the top or from the antitop quarks and the cross section is directly proportional to the top-quark Yukawa coupling [4, 5]. We mainly focus on a Standard Model (SM) like Higgs boson (H = hSM ), giving only some qualitative indication of how the analysis could be generalized to the Minimal Supersymmetric Standard Model (MSSM) Higgs sector (H = h0 , H 0 , A0 ). In our analysis we consider the Higgs boson decaying into b¯b, γγ, and τ + τ − and we determine the significance of the signal over the background in these three cases. As a result, all three channels turn out to be viable, even for fairly low integrated luminosities, providing a determination of the top-quark Yukawa coupling at the few percent level over a large range of Higgs boson masses. The layout of our presentation is as follows. The characteristics of the the associated production of a SM like Higgs boson in pp → tt¯H are described in Sec. II. In Sec. III we compare signal and background, in the SM, for the three Higgs boson decay channels discussed above, and estimate the relative error with which the SM top-quark Yukawa coupling could be measured at a VLHC. We also give some qualitative indications of how the results could change if the MSSM Higgs sector is considered. Sec. IV contains our conclusions.

∗ [email protected] † [email protected] ‡ [email protected]

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II.

FIG. 2: Total cross section for pp → tt¯hSM as a function of MhSM , for various center of mass energies.

SIGNAL

The total hadronic cross section for pp → tt¯H (H = hSM , h0 , H 0 , A0 ) consists of two parton level sub-processes: q q¯ → tt¯H and gg → tt¯H. Taking H = hSM for illustrative purposes, we plot in Fig. 1 the relative contribution of the two subprocesses, for MH = 150 GeV. As expected, the gg contribution dominates as the center of mass energy is increased. √ In Fig. 2 we also show√the dependence of the total cross section from MH , again when H = hSM , for s = 14 TeV √ (LHC) and s = 40, 100, 200 TeV (VLHC). For the highest center of mass energy considered in this paper, s = 200 TeV, the total cross section is enhanced by two to three orders of magnitude with respect to the corresponding cross section at the LHC, depending on the Higgs boson mass. All the results presented in this paper are obtained using tree-level cross sections, both for the signal and for the backgrounds, calculated using CTEQ4L [6] parton distribution functions and the strong coupling constant αs (µ) at one-loop. As usual, tree-level cross sections have a very large renormalization/factorization scale dependence and, as a result, a large uncertainty. At present, only the next-to-leading QCD corrections to the signal are known [7, 8, 9]. Since we do not aim at a precise determination of the cross section, but at a study of signal vs. background, we prefer to consistently use only quantities calculated at leading order, without including any K-factors. The renormalization and factorization scales have been set to a common value µ = mt + MH /2, with mt = 174 GeV. III.

SIGNAL VS. BACKGROUND FOR VARIOUS DECAY CHANNELS

In this section we present some studies of the irreducible backgrounds and discuss the expected precision with which a measurement of the SM top-quark Yukawa √coupling can be performed at a VLHC. For illustration purposes, we consider the case of a VLHC operating at s = 100 TeV. In Fig. 3 we compare the cross sections for the signal, pp → tt¯hSM , and for the irreducible backgrounds consisting of tt¯XX production with X = b, γ, τ [17]. The cross sections for the signal include the branching ratios hSM → XX, calculated using HDECAY [10]. In order to take into account finite mass resolution effects, the background events are plotted in bins of 40, 5, and 20 GeV for b, γ, and τ respectively. To simulate the detector acceptance, the decay products of the Higgs boson are required to have a transverse momentum pT > 25 GeV and a pseudorapidity |η| < 3. The set of parton distribution functions is CTEQ4L and the renormalization and factorization scales are set equal to mt + MXX /2, where MXX is the invariant mass of the XX pair. Qualitatively, the signal to background ratios

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are similar to those expected at the LHC [11]. For the leading decay channel hSM → b¯b the QCD background is comparable to the signal, while for the hSM → γγ and hSM → τ + τ − decay channels the background is small, if not negligible. However, for these last two channels, the advantage √ of a VLHC over the LHC is manifest. Already with 100 fb−1 of integrated luminosity, at a VLHC with s = 100 TeV, the number of signal events is increased by about a factor of 50 − 100 (for MhSM = 100 − 200 GeV) with respect to the LHC, therefore allowing studies that are statistically limited at the LHC. Even for the hSM → b¯b decay channel, assuming that efficiencies similar to those at the LHC could be attained, the significance of the signal (directly related to the √ accuracy with which the top Yukawa coupling can be measured) would be increased by a factor ≃ 50. A first TABLE I: Number of signal√events for tt¯hSM , MhSM = 130 GeV, and irreducible tt¯XX background events with X = b, γ, τ , at a VLHC with s = 100 TeV and integrated luminosity of 100 fb−1 . Same conventions as in Fig. 3. In the total number of events the branching ratios for hSM → XX with X = b, γ, τ are included. In the second line the top-quark and τ branching ratio into final states are included. Detector and reconstruction efficiencies are estimated from LHC studies (e.g., [11]) and inserted in the third line. In the last line, (one half of) the relative error on the measurement of the cross section is quoted. This is directly related to the precision on the extraction of the Yukawa coupling of the p top, δyt /yt = (δσ/2σ)2 + (δyX /yX )2 , and corresponds to it when the uncertainty on the branching ratios of the Higgs into the final states is negligible. b¯b S

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estimate of the √ precision with which the SM top-quark Yukawa coupling could be measured at a VLHC is given in Table I, for s = 100 TeV and MhSM = 130 GeV. In our analysis we assume 100 fb−1 of total integrated luminosity, corresponding to roughly one year of running of a VLHC with luminosity L = 1034 cm−2 s−1 . In analogy with similar studies performed for the LHC [11, 12, 13], we consider a sample where one top quark decays leptonically, in order to have an unambiguous lepton tag, and the other top decays hadronically. We apply a tt¯ pair reconstruction efficiency ǫtt¯ = 0.15. We also use a b tagging efficiency ǫb = 0.6, a τ tagging efficiency ǫτ = 0.6, and a photon identification efficiency ǫγ = 0.9. Moreover, in order to account for the efficiency

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FIG. 4: Cross sections for tt¯hSM √ (thin solid line) and tt¯H(H = h0 , H 0 and A0 ) production (thick black, dark-grey and light-grey lines), at a VLHC with s = 100 TeV: A) total cross sections; B)-D) cross sections times branching ratios for H → b¯b, γγ, τ + τ − respectively.

of the invariant mass finite cut imposed by the binning procedure, we multiply the results for the tt¯b¯b and γ ¯ ¯¯ tt¯τ + τ − signatures by ǫb,τ mc = 0.7, and the results for the ttγγ signature by ǫmc = 0.9 . The ttbb signature is further reduced by a factor ǫcomb = 0.5, to take into account the combinatorics due to the four b quarks in the final state. Finally, we only consider the tt¯τ + τ − signature where the τ ’s decay hadronically and we therefore multiply by Br(τ → hadrons) = 0.63 for each τ lepton in the final state [18]. As a result, the statistical error on the tt¯hSM production cross section for a SM Higgs boson with mass 130 GeV is at the percentage level for both the tt¯b¯b and tt¯τ + τ − signatures, while for the tt¯γγ signature is around 10%. The precision with which the top-quark Yukawa coupling can be extracted from the measured tt¯hSM cross section depends on the accuracy on the hSM → XX branching ratios (see Table I). Assuming that all other Higgs boson couplings entering our analysis have been determined with very good precision, then all three signatures allow a measurement of the top Yukawa coupling with precision better than 10%, for Higgs boson masses up to 150 GeV. We note that the level of precision obtained is comparable with the precision √ that could be attained at a high energy Linear Collider, running at the optimal center of mass energy of s = 800 GeV, when 103 fb−1 of integrated luminosity are used [14, 15]. On the other hand, our results are obtained using a quite low integrated luminosity, 102 fb−1 , and could therefore be further improved by more available statistics. Finally, it is worth having a quick look at tt¯H production in the MSSM (for H = h0 , H 0 , A0 ). For the MSSM

5 scenario we assume some √ “typical” set of parameters: tan β = 40, mq˜ = 500 GeV, µ = 300 GeV, At = Ab = A with A = µ/ tan β + 6mq˜, according to the “maximal mixing” scenario where loop corrections maximize the light Higgs boson mass. The total cross sections for the signal tt¯H as well as the total cross sections multiplied by the branching ratios for H → b¯b, γγ, τ + τ − are presented in Fig. 4. The cross sections for tt¯h0 and tt¯hSM are close to each other in the narrow, but crucial, region up to MH = 120 GeV or slightly above that. However, we note that, when the branching ratios are included, both the tt¯b¯b and tt¯τ + τ − MSSM signatures for h0 are 30-40% higher than the corresponding SM signatures. Above 120 GeV only the tt¯H 0 and tt¯A0 associated production can take place. The tt¯H 0 signal is suppressed by a factor of cos β 2 compared to the corresponding SM signal. It is similar to the light Higgs boson (h0 ) signal only in the small region around 120 GeV, where all three MSSM Higgs bosons are degenerate in mass. For MH > 120 GeV the tt¯H 0 cross section drops rapidly and becomes comparable to the tt¯A0 cross section for Higgs boson masses above 200 GeV. The cross sections for both tt¯H 0 and tt¯A0 above 120 GeV are 2-3 orders of magnitude below the SM cross section. However, when we take into account the corresponding Higgs boson decay branching ratios, the situation can be very different. For instance, when H → τ + τ − , the MSSM cross sections start dominate the SM one over the entire mass region MH > 200 GeV. This happens because the MSSM H → τ + τ − branching ratio is significant over the entire Higgs boson mass region for high tan β. With this respect, the tt¯τ + τ − supersymmetric signature (summed over the tt¯A0 and tt¯H 0 channels) could be interesting in the high MSSM Higgs boson mass range (MH ≥ 200 GeV). Since however, even at a VLHC, this channel appears to be statistically limited, it will require a large integrated luminosity. We note that the MSSM tt¯b¯b signature also dominates over the SM one for large Higgs masses, but in this case, contrary to tt¯τ + τ − , the background is overwhelming. IV.

CONCLUSIONS

In this note we have studied the precision with which the top-quark Yukawa coupling could be determined at a pp VLHC through the measurement of the cross section for the process pp → tt¯H, with the Higgs boson subsequently decaying into b¯b, γγ, and τ + τ − . We have mainly focused on a SM like Higgs boson, but have also looked at some interesting MSSM signatures, for both light and heavy Higgs bosons. Assuming that the branching ratios of the Higgs into the final states were known with very good precision, each of the three Higgs boson decay channels could provide a determination of the top-quark Yukawa coupling at the few percent level, over a large range of Higgs boson masses. In particular, the γγ and τ + τ − channels, which will be statistically limited at the LHC, are at the VLHC very clean and already significant with just 100 fb−1 of integrated luminosity. This could be extremely useful, even under the pessimistic assumption that some of the Higgs boson branching ratios had still to be determined by the VLHC era. For instance, the determination of yt from the γγ and/or τ + τ − channels, could be used to extract the branching ratio of the Higgs into ¯bb, which will be hard to measure directly at the LHC. Or, one could directly check that the ratio Γ(H → b¯b)/Γ(H → τ + τ − ) behaves as m2b /m2τ , and subsequently extract the top Yukawa coupling yt by following a strategy similar to the one suggested in Ref. [16]. Acknowledgments

We are grateful to David Rainwater for his comments and suggestions. The work of A.B. and L.R. (F.M.) is supported in part by the U.S. Department of Energy under contract No. DE-FG02-97ER41022 (DE-FG0291ER40677).

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A. Djouadi, J. Kalinowski, and M. Spira, Comput. Phys. Commun. 108, 56 (1998), arXiv:hep-ph/9704448. M. Beneke et al., Top quark physics (2000), arXiv:hep-ph/0003033. CMS Collaboration, Tech. Rep. CERN/LHCC/94-38, CERN (1994). ATLAS Collaboration, Tech. Rep. CERN/LHCC/99-15, CERN (1999). H. Baer, S. Dawson, and L. Reina, Phys. Rev. D61, 013002 (2000), arXiv:hep-ph/9906419. A. Juste and G. Merino (1999), arXiv:hep-ph/9910301. D. Zeppenfeld, R. Kinnunen, A. Nikitenko, and E. Richter-Was, Phys. Rev. D62, 013009 (2000), hep-ph/0002036. Even though we do not include in this study other decay modes, such as, for instance, hSM → W W, ZZ, they are potentially interesting and more detailed analysis are in progress. [18] In a more complete analysis other data samples should be added to this channel. For instance, the case where one τ decays leptonically, providing the lepton tag, and both the top quarks decay hadronically has a comparable rate.